Find the greatest common factor of $7, 15,$ and $21$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of $7, 15,$ and $21$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}7 &=7\\\\\\\\ 15&=3\cdot5\\\\\\\\ 21&=3\cdot7 \end{aligned}$ Since these numbers have no common prime factors, we say that the GCF is $1$. This is because all numbers share a factor of $1$ : $ \begin{aligned}7 &=7\cdot1\\\\\\\\ 15&=3\cdot5\cdot1\\\\\\\\ 21&=3\cdot7\cdot1 \end{aligned}$ The greatest common factor of $7, 15,$ and $21$ is $1$.